The 28-year-old has struggled at both Sunderland and Hull, but he produced a fine strike early in the first half at the Liberty Stadium to put his name on the scoresheet for the first time since he netted for Swansea in a League Cup win at Chelsea in January.
Graham's first goal for Hull wasn't enough to secure the points however as Swansea defender Chico Flores equalised in the second half.
The result left both sides in mid-table, with 10th placed Swansea one point above their opponents.
"Certainly it's been a long-time coming," Graham said of a 30-game drought that lasted 1,626 minutes. "I wanted to go crazy when I scored but I had a good relationship with the Swansea fans and had good times down here so I wasn't going to celebrate." Michael Laudrup, Swansea's manager, added: "In the second half we did much better and got the equaliser, but after such a bad first half we didn't deserve to win today."
Swansea forward Michu was back in the team after five weeks out with an ankle injury. But it took Graham just nine minutes to show his old employers the sort of predatory finishing he produced on a regular basis during his time in south Wales.
Swansea defender Ashley Williams contributed to his side's downfall with a careless pass to Ahmed Elmohamady.
Elmohamady raced down the right flank before whipping over a cross to the far post, where Graham had found space to guide a left-foot volley past Gerhard Tremmel from close-range.
Graham could have been forgiven for embarking on a jubilant celebration after ending his long drought, but instead he showed his respect for Swansea by putting his hands in the air in a gesture of apology.
Williams had an opportunity to atone for his earlier blunder when Jonathan De Guzman's corner dropped to him in the Hull penalty area, but the Wales international dragged his shot well wide.
That summed up a lacklustre first-half for Swansea, who dominated possession without threatening to break down Hull's defence. Tom Huddlestone wasted a golden chance to double Hull's lead when he sliced over from 12 yards, and Swansea made the most of that escape as they grabbed a fortuitous equaliser on the hour.